A340306 Numbers k such that A065642(k) = A081761(k).

12, 420, 540, 2268, 7020, 10692, 11340, 17640, 24948, 42750, 56700, 87120, 152460, 409500, 413100, 609840, 996072, 2478600, 3822000, 5287500, 9189180, 9447840, 14871600, 20241900, 20567520, 23510592, 23832800, 27766152, 28552500, 39358800, 41135040, 44783648, 49985100

Offset: 1

Author

Amiram Eldar, Jan 03 2021

Keywords

• nonn

Comments

Numbers k such that the least number that is larger than k and has the same prime signature as k and the least number that is larger than k and has the same set of distinct prime divisors as k are equal.

Examples

			12 is a term since the A065642(12) = A081761(12) = 18, i.e., 18 = 2 * 3^2 is the least number with the same set of prime divisors, {2, 3}, and the same prime signature as 12 = 2^2 * 3.
		

Links

• Index entries for sequences related to prime signature

Crossrefs

Intersection of A340302 and A340305.

Cf. A065642, A081761.

Programs

Mathematica

rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; next[n_] := Module[{r = rad[n]}, SelectFirst[Range[n + 1, n^2], rad[#] == r &]]; sig[n_] := Sort@FactorInteger[n][[;; , 2]]; nextsig[n_] := Module[{sign = sig[n], k = n + 1}, While[sig[k] != sign, k++]; k]; Select[Range[2, 600], sig[#] == sig[next[#]] && rad[#] == rad[nextsig[#]] &]